Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1516576 | Journal of Physics and Chemistry of Solids | 2012 | 5 Pages |
The Hohenberg–Kohn theorem is generalized to the case of electrons in the presence of both an external electrostatic E(r)=−∇v(r)E(r)=−∇v(r) and magnetostatic B(r)=∇×A(r)B(r)=∇×A(r) field. For the non-degenerate ground state, it is established that the basic variables are the ground state density ρ(r)ρ(r) and physical current density j(r)j(r) by proving the relationship between the densities {ρ(r),j(r)}{ρ(r),j(r)} and the external potentials {v(r),A(r)}{v(r),A(r)} is one-to-one . A constrained-search proof is also provided. It is further explained why the basic variables cannot be the density ρ(r)ρ(r) and the paramagnetic current density jp(r)jp(r) as presently thought to be the case.
► The Hohenberg–Kohn theorem is generalized to electrons in an external magnetostatic field. ► For the non-degenerate ground state, the relationship between the physical densities {ρ(r),j(r)}{ρ(r),j(r)} and potentials {v(r),A(r)}{v(r),A(r)} is one-to-one. ► A constrained-search proof is also provided. ► We explain why ρ(r)ρ(r) and the paramagnetic current density jp(r)jp(r) cannot be basic variables.